Question 884242
Complete the square to get into vertex form.
{{{y=-2x^2+8x+5}}}
{{{y=-2(x^2-4x)+5}}}
{{{y=-2(x^2-4x+4)+5+2(4)}}}
{{{y=-2(x-2)^2+13}}}
Since the multiplier on the {{{(x-2)^2}}} term is negative, it opens downwards.
The vertex is ({{{2}}},{{{13}}}).
The axis of symmetry is {{{x=2}}}.
The y intercept is 
{{{y=-2(0-2)^2+13}}}
{{{y=-8+13}}}
{{{y=5}}}
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{{{drawing(300,300,-4,8,-30,20,grid(1),circle(2,13,0.3),circle(0,5,0.3),blue(line(2,-40,2,40)),graph(300,300,-4,8,-30,20,-2x^2+8x+5))}}}